What is the general solution for sin(x)= 15/18 ?

The general solution for sin(x)= 15/18 is x=0.98511…+2pin,x=pi-0.98511…+2pin

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sin(x)= 15/18

sin (x) = \frac{15}{18}

x = 0.98511 \dots + 2 πn, x = π - 0.98511 \dots + 2 πn

Solution steps

sin (x) = \frac{15}{18}

Cancel the common factor:

3

sin (x) = \frac{5}{6}

Apply trig inverse properties

x = arcsin (\frac{5}{6}) + 2 πn, x = π - arcsin (\frac{5}{6}) + 2 πn

Show solutions in decimal form

x = 0.98511 \dots + 2 πn, x = π - 0.98511 \dots + 2 πn

cos (5 x) = cos (5 + x)

6 cos^{2} (x) - 7 cos (x) - 5 = 0

cos (x) = \frac{- 3}{5 sin ^{2} ( x )}

5 cos^{2} (x) - 12 sin^{2} (x) = 13

cos^{2} (x) - 0.5 cos (x) = 0

What is the general solution for sin(x)= 15/18 ?
The general solution for sin(x)= 15/18 is x=0.98511…+2pin,x=pi-0.98511…+2pin